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On interval routing schemes and treewidth. (English) Zbl 0892.68069
Summary: We investigate which processor networks allow $$k$$-label interval routing schemes, under the assumption that costs of edges may vary. We show that for each fixed $$k\geq 1$$, the class of graphs allowing such routing schemes is closed under minor-taking in the domain of connected graphs, and hence has a linear time recognition algorithm. This result connects the theory of compact routing with the theory of graph minors and treewidth. We show that every graph that does not contain as a minor has treewidth at most $$2r- 2$$. As a consequence, graphs that allow $$k$$-label interval routing schemes under dynamic cost edges have treewidth at most $$4k$$. Similar results are shown for other types of interval routing schemes.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science
##### Keywords:
interval routing schemes
Full Text:
##### References:
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